New Jacobian Elliptic Function Solutions to Modified KdV Equation: I**The project supported by National Natural Science Foundation of China under Grant No. 10072013 and the National Key Basic Research Development Project Program under Grant No. G1998030600

Abstract

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdV equation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to other nonlinear differential equations.